If the covariance of returns between two equally-weighted securities A & B, whose standard deviations are 13% and 5% respectively, is −0.0080, the expected standard deviation of the portfolio is closest toQuestion 25Answera.1.65%b.2.91%c.0.085%
Question
If the covariance of returns between two equally-weighted securities A & B, whose standard deviations are 13% and 5% respectively, is −0.0080, the expected standard deviation of the portfolio is closest toQuestion 25Answera.1.65%b.2.91%c.0.085%
Solution
The standard deviation of a two-asset portfolio can be calculated using the formula:
σp = sqrt[(w1^2 * σ1^2) + (w2^2 * σ2^2) + (2 * w1 * w2 * Cov1,2)]
where:
- w1 and w2 are the weights of the two assets in the portfolio (in this case, both are 0.5 because the assets are equally weighted),
- σ1 and σ2 are the standard deviations of the two assets (13% and 5% respectively), and
- Cov1,2 is the covariance of the returns of the two assets (-0.0080).
Substituting the given values into the formula, we get:
σp = sqrt[(0.5^2 * 0.13^2) + (0.5^2 * 0.05^2) + (2 * 0.5 * 0.5 * -0.0080)] = sqrt[(0.25 * 0.0169) + (0.25 * 0.0025) - 0.004] = sqrt[0.004225 + 0.000625 - 0.004] = sqrt[0.00085]
So, the standard deviation of the portfolio is sqrt[0.00085] = 0.0291 or 2.91%.
Therefore, the correct answer is b. 2.91%.
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